A theory of neocortical seizure spread: Insights from statistical physics

Abstract

42The conception of seizures as abnormal synchronies of large neuronal populations has 43 been confirmed by numerous electrophysiological studies, including recent imaging of travelling 44 seizure waves across the neocortex. This traditional viewpoint has been challenged by the 45 finding that during some seizures, neurons with high firing rates are remarkably rare and sparsely 46 distributed into clusters. Reconciliation of these seemingly contradictory descriptions has 47 attracted much attention, raising questions such as how (or if) macroscopic seizure waves arise 48 from these microscope neuronal clusters, and more generally, how other features of macroscopic, 49 clinical seizures arise from microscopic dynamics. Answers to these questions are crucial to the 50 understanding of epilepsy, and could guide development of drugs and other interventions that act 51 at the microscopic level to effect macroscopic improvement. 52Relationships between microscopic and macroscopic processes are addressed by the field 53 of statistical physics, offering explanations for how macroscopic quantities such as pressure and 54 temperature arise from microscopic interactions between molecules. Here we hypothesize that 55 these methods could also provide insight between the macroscopic and microscopic dynamics of 56 seizure behavior. We constructed a model of the neocortex composed of small domains, each 57 representing a cluster of neurons. Models with and without refractory periods were studied.58 Allowing seizures to spread among the clusters in a probabilistic fashion produced a "cellular 59 automaton" amenable to the methods of statistical physics. We thereby showed that the model 60 harbors a continuous phase transition allowing possible explanations for the emergence of 61 seizure waves from microscopic neuronal clusters, and for a surprisingly wide variety of seizure 62 properties. Moreover, the model is easy to use because it requires only a small number of 63 intuitively understood rules and is computationally efficient. We hope that these insights from 3 64 statistical physics will contribute to the understanding of epilepsy and to the identification of new 65 therapeutic measures. 66 67 68 69 70 71 Author summary 72 Epilepsy is a common neurological disease characterized by devastating, unpredictable 73 seizures. Extensive research is aimed at improving the treatment of epilepsy through better 74 understanding of how seizures start and spread, but basic questions remain unanswered. Do 75 seizures start as waves of overactive neuronal activity, or as small clusters of activity as 76 suggested by recent data? How do clinical properties of seizures emerge from interactions 77 between small groups of neurons? And would understanding this emergence lead to better 78 treatment? 79 We address these questions with a mathematical model of seizure spread, using methods 80 of physics designed to explain how quantities such as pressure and temperature emerge from 81 interactions between molecules. The model produced small cluster...